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KIMIA ORGANIK FISIK
Edy Cahyono
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KIMIA ORGANIK FISIK
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Review:
Hibridisasi, resonansi, konjugasi, hiperkonjugasi (1).
Reaksi dasar organik, kinetika, energetika, stereokimia, dan
mekanisme reaksi (2).
Mekanisme Substitusi (3,4).
Mekanisme Eliminasi (5).
Faktor-faktor yang menentukan mekanisme reaksi (6)
Mekanisme reaksi radikal bebas (7).
Mid semester (8).
Reaksi adisi pada alkena (9,10,11)
Reaksi adisi pada gugus karbonil (12, 13)
Reaksi perisiklik (14)
Reaksi polimerisasi (15)
Sumber belajar:
Peter Sykes, Penuntun mekanisme reaksi organik, hal 1-100
Fessenden, Kimia Organik I, Bab Alkil halida
Chapter 1 Bonding and Geometry
Organic Chemistry
• The study of the compounds of carbon.
• Over 10 million compounds have been identified.
– About 1000 new ones are identified each day!
• C is a small atom.
– It forms single, double and triple bonds.
– It is intermediate in electronegativity (2.5).
– It forms strong bonds with C, H, O, N, and some
metals.
Schematic View of an Atom
• A small dense nucleus, diameter 10-14 - 10-15 m,
which contains positively charged protons and
most of the mass of the atom.
• An extranuclear space, diameter 10-10 m, which
contains negatively charged electrons.
Lewis Dot Structures
• Gilbert N. Lewis
• Valence shell:
– The outermost occupied electron shell of an
atom.
• Valence electrons:
– Electrons in the valence shell of an atom; these
electrons are used to form chemical bonds and
in chemical reactions.
• Lewis dot structure:
– The symbol of an element represents the
nucleus and all inner shell electrons.
– Dots represent electrons in the valence shell of
the atom.
Lewis Dot Structures
• Table 1.4 Lewis Dot Structures for Elements 1-18
1A
Na
4A
5A
6A
7A
.
8A
.
.
Be
Mg
:
:
.
B
.
Al
:
.
C:
.
.
. N. :
.
: O. :
.
:..F :
:
.
Si :
.
.
. .P :
.
: S. :
.
:Cl :
:
: :
He
:N e :
: :
Li
3A
:
H
2A
:A r :
Lewis Model of Bonding
• Atoms interact in such a way that each participating
atom acquires an electron configuration that is the
same as that of the noble gas nearest it in atomic
number.
– An atom that gains electrons becomes an anion.
– An atom that loses electrons becomes a cation.
– The attraction of anions and cations leads to the
formation of ionic solids. This ionic interaction is often
referred to as an ionic bond.
– An atom may share electrons with one or more atoms to
complete its valence shell; a chemical bond formed by
sharing electrons is called a covalent bond. Bonds may
be partially ionic or partially covalent; these bonds are
called polar covalent bonds
Electronegativity
• Electronegativity:
– A measure of an atom’s attraction for the
electrons it shares with another atom in a
chemical bond.
• Pauling scale
– Generally increases left to right in a row.
– Generally increases bottom to top in a column.
Formation of Ions
A rough guideline:
• Ions will form if the difference in electronegativity
between interacting atoms is 1.9 or greater.
• Example: sodium (EN 0.9) and fluorine (EN 4.0)
• We use a single-headed (barbed) curved arrow to
show the transfer of one electron from Na to F.
+
F
••
+
Na
••
-
•
•
•
•
Na
•
•
••
F
••
• In forming Na+F-, the single 3s electron from Na is
transferred to the partially filled valence shell of F.
Na(1 s 22s 22p 63s 1) + F(1s 2 2s 2 2p 5 )
Na + (1s 22s 22p 6) + F-(1s 2 2s 2 2p 6 )
Covalent Bonds
• The simplest covalent bond is that in H2
– The single electrons from each atom combine to form
an electron pair.
H•
+
•H
H-H
H0 = -435 kJ (-104 kcal)/mol
– The shared pair functions in two ways simultaneously; it
is shared by the two atoms and fills the valence shell of
each atom.
• The number of shared pairs
– One shared pair forms a single bond
– Two shared pairs form a double bond
– Three shared pairs form a triple bond
Polar and Nonpolar Covalent Bonds
• Although all covalent bonds involve sharing
of electrons, they differ widely in the degree
of sharing.
• We divide covalent bonds into nonpolar
covalent bonds and polar covalent bonds.
D i fference in
El ectron eg ati vity
Betw een Bo nded Ato ms
Less than 0.5
0.5 to 1.9
Greater than 1.9
Typ e of Bond
N on pol ar cov alent
Pol ar co valent
Io ns f orm
Polar and Nonpolar Covalent Bonds
• An example of a polar covalent bond is that of H-Cl.
• The difference in electronegativity between Cl and
H is 3.0 - 2.1 = 0.9.
• We show polarity by using the symbols d+ and d-,
or by using an arrow with the arrowhead pointing
toward the negative end and a plus sign on the tail
of the arrow at the positive end.
d+
H
dCl
H
Cl
Polar Covalent Bonds
Bond dipole moment (m):
• A measure of the polarity of a covalent bond.
• The product of the charge on either atom of a polar
bond times the distance between the two nuclei.
• Table 1.7
Bond
Dipole
Bond (D )
Bond
Dipole
Bond (D )
Bond
D ipole
Bond (D)
H-C
H-N
H-O
H-S
C-F
C-Cl
C-Br
C-I
C-O
C=O
C-N
-C=N
0.3
1.3
1.5
0.7
1.4
1.5
1.4
1.2
0.7
2.3
0.2
3.5
Lewis Structures
• To write a Lewis structure
– Determine the number of valence electrons.
– Determine the arrangement of atoms.
– Connect the atoms by single bonds.
– Arrange the remaining electrons so that each
atom has a complete valence shell.
– Show a bonding pair of electrons as a single line.
– Show a nonbonding pair of electrons (a lone
pair) as a pair of dots.
– In a single bond atoms share one pair of
electrons, in a double bond they share two pairs
of electrons and in a triple bond they share three
pairs of electrons.
Lewis Structures - Table 1.8
H-O-H
H-N-H
H
H 2 O (8)
Water
H
N H 3 (8)
Ammonia
H
C C
H
H
C2 H 4 (12)
Ethylene
H
H-C-H
H
CH 4 (8)
Meth ane
H-Cl
HCl (8)
Hyd rogen ch loride
O
H
H-C C-H
C O
C2H 2 (10)
Acetylen e
H
CH 2O (12)
Formald ehyde
H
O
C
O
H
H 2CO 3 (24)
Carbonic acid
• In neutral molecules
–
–
–
–
–
hydrogen has one bond.
carbon has 4 bonds and no lone pairs.
nitrogen has 3 bonds and 1 lone pair.
oxygen has 2 bonds and 2 lone pairs.
halogens have 1 bond and 3 lone pairs.
Formal Charge
• Formal charge: The charge on an atom in a
molecule or a polyatomic ion.
• To derive formal charge
1. Write a correct Lewis structure for the molecule or ion.
2. Assign each atom all its unshared (nonbonding)
electrons and one-half its shared (bonding) electrons.
3. Compare this number with the number of valence
electrons in the neutral, unbonded atom.
Formal
charge
N umber of
= valence electrons
in th e neutral,
un bonded atom
All
One h alf of
un shared + all sh ared
electrons
electrons
4. The sum of all formal charges is equal to the total charge
on the molecule or ion.
Formal Charge
• Example: Draw Lewis structures, and show
which atom in each bears the formal charge.
(a) NH2
-
(d) CH3 NH3
(b) HCO3
+
-
(c) CO3
-
(e) HCOO
2-
-
(f) CH3 COO
Apparent Exceptions to the Octet Rule
• Molecules that contain atoms of Group 3A
elements, particularly boron and aluminum.
B
Boron trifluoride
: Cl
Al
: Cl :
:
:
:F:
: Cl :
: :
: :
:F
:
:
: F:
6 electrons in the
valence shells of boron
and aluminum
Aluminum chloride
Apparent Exceptions to the Octet Rule
:
• Atoms of third-period elements are often drawn
with more bonds than allowed by the octet rule.
• The P in trimethylphosphine obeys the octet rule
by having three bonds and one unshared pair.
• A common depiction of phosphoric acid, however,
has five bonds to P, which is explained by invoking
the use of 3d orbitals to accommodate the
additional bonds.
:
H- O-P- O-H
:
Cl :
:
Cl :
:O:
: :
: Cl
P
: : : :
O-H
Phosphoric
acid
:
CH3
Trimethylphosphine
: : : :
:
CH3 -P- CH3
: Cl
Cl :
Phosphorus
pentachloride
Apparent Exceptions to the Octet Rule
• However, the use of 3d orbitals for bonding is in
debate.
• An alternative representation that gives P in
phosphoric acid an octet has four bonds and a
positive formal charge on P. The oxygen involved in
the double bond of the alternative depiction has one
bond and a negative formal charge.
O
HO
P
OH
formal
charges
O
OH
HO
P
OH
OH
Apparent Exceptions to the Octet Rule
H 3C
S
CH3
H 3C
S
:
H
CH3
Dimethyl sulfoxide
:
Hydrogen
sulfide
OH
:O :
HO
:O :
:
HO
: :
: :
S
S +2
Sulfuric acid
::
:O:
:O :
: :
S
formal
charges
:O :
:O :
:
H
: :
:
• Sulfur is commonly depicted with varying numbers
of bonds. In each of the alternative structures, sulfur
obeys the octet rule.
OH
formal
charges
Alcohols
• Contain an -OH (hydroxyl) group bonded to a
tetrahedral carbon atom.
H H
:
-C-O-H
:
H-C-C-O-H
Fu nctional
group
H H
Ethan ol
(an alcohol)
• Ethanol may also be written as a condensed
structural formula.
CH3 -CH2 -OH
or
CH3 CH2 OH
Alcohols
• Alcohols are classified as primary (1°), secondary
(2°), or tertiary (3°) depending on the number of
carbon atoms bonded to the carbon bearing the OH group.
H
CH3 -C-OH
H
A 1° alcohol
H
CH3 -C-OH
CH3
A 2° alcohol
CH3
CH3 -C-OH
CH3
A 3° alcohol
Alcohols
There are two alcohols with molecular formula C3H8O
HHH
H-C-C-C-O-H
or CH3 CH2 CH2 OH
H HH
a 1° alcohol
H
HOH
H C-C-C-H
HH H
or
OH
CH3 CHCH3
a 2° alcohol
Amines
• Contain an amino group; an sp3-hybridized
nitrogen bonded to one, two, or three carbon
atoms.
– An amine may by 1°, 2°, or 3°.
Methylamine
(a 1° amine)
CH3 N H
CH3
Dimethylamine
(a 2° amine)
:
H
:
:
CH3 N H
CH3 N CH3
CH3
Trimethylamine
(a 3° amine)
Aldehydes and Ketones
• Contain a carbonyl (C=O) group.
: O:
C
O
H
CH3 -C- H
Functional Acetaldehyde
(an aldehyde)
group
:O:
O
C
CH3 -C- CH3
Functional Acetone
(a ketone)
group
Carboxylic Acids
• Contain a carboxyl (-COOH) group.
:
Fu nctional
group
:O:
CH3 -C-O-H
:
O
C O H
or CH3 COOH or CH3 CO2 H
Acetic aci d
(a carboxy li c acid )
Carboxylic Esters
• Ester: A derivative of a carboxylic acid in
which the carboxyl hydrogen is replaced by a
carbon group.
O
C O
Functional
group
O
CH3 - C-O- CH 2 -CH3
Ethyl acetate
(an ester)
Carboxylic Amide
• Carboxylic amide, commonly referred to as an
amide: A derivative of a carboxylic acid in which
the -OH of the -COOH group is replaced by an
amine.
O
C N
Fu nctional
group
O
CH3 -C-N-H
H
Acetamid e
(a 1° amid e)
– The six atoms of the amide functional group lie
in a plane with bond angles of approximately
120°.
VSEPR
• Based on the twin concepts that
– atoms are surrounded by regions of electron
density.
– regions of electron density repel each other.
H
C
H
H
: :
: :
O C
C
H
O
H
H
H
H
C
H
H
H
H
C
O
N
:
H
2 region s of e - d ensity
(lin ear, 180°)
H H
H
H
C
N
: :
3 region s of e - d ensity
(trigon al planar, 120°)
:
4 region s of e - d ensity
(tetrahed ral, 109.5°)
H
O H C C H H C N
VSEPR Model
• Example: predict all bond angles for these
molecules and ions.
( a) NH4 +
( b ) CH3 NH 2
( d ) CH3 OH
( e) CH 3 CH= CH 2
( f ) H 2 CO 3
( g ) HCO 3 -
( h) CH3 CHO
( i) CH 3 COOH
( j ) BF4 -
Polar and Nonpolar Molecules
• To determine if a molecule is polar, we need
to determine
– if the molecule has polar bonds and
– the arrangement of these bonds in space.
• Molecular dipole moment (m): The vector sum
of the individual bond dipole moments in a
molecule.
– reported in Debyes (D)
Electrostatic Potential (elpot) Maps
• In electrostatic potential maps (elpots)
– Areas of relatively high calculated electron
density are shown in red.
– Areas of relatively low calculated electron
density are shown in blue.
– Intermediate electron densities are represented
by intermediate colors.
Polar and Nonpolar Molecules
• These molecules have polar bonds, but each
molecule has a zero dipole moment.
Cl
F
O
C
B
O
F
F
Carbon dioxide
m=0D
Boron trifluoride
m=0D
C
Cl
Cl
Cl
Carbon tetrachloride
m=0D
Polar and Nonpolar Molecules
• These molecules have polar bonds and are polar
molecules.
direction
of dip ole
moment
N
O
H
H
Water
m = 1.85D
H
H
Ammonia
m = 1.47D
H
direction
of dip ole
moment
Polar and Nonpolar Molecules
• Formaldehyde has polar bonds and is a polar
molecule.
direction
of dip ole
moment
O
H
C
H
Formaldehyde
m = 2.33 D
Shapes of Atomic s and p Orbitals
• All s orbitals have the
shape of a sphere with
the center of the
sphere at the nucleus.
Shapes of Atomic s and p Orbitals
– Figure 1.9 (a) 3D representations of the
2px, 2py, and 2pz atomic orbitals including
nodal planes.
Shapes of Atomic s and p Orbitals
• Figure 1.9(b) Cartoon representations of the
2px, 2py, and 2pz atomic orbitals.
Molecular Orbital Theory
• MO theory begins with the hypothesis that
electrons in atoms exist in atomic orbitals and
electrons in molecules exist in molecular
orbitals.
Molecular Orbital Theory
Rules:
• Combination of n atomic orbitals gives n MOs.
• MOs are arranged in order of increasing energy.
• MO filling is governed by the same rules as for
atomic orbitals:
• Aufbau principle: fill beginning with LUMO
• Pauli exclusion principle: no more than 2e- in
a MO
• Hund’s rule: when two or more MOs of
equivalent energy are available, add 1e- to
each before filling any one of them with 2e-.
Molecular Orbital Theory
• Figure 1.10 MOs derived from combination by (a)
addition and (b) subtraction of two 1s atomic
orbitals.
Covalent Bonding-Combined VB & MO
• Bonding molecular orbital: A MO in which
electrons have a lower energy than they
would have in isolated atomic orbitals.
• Sigma (s) bonding molecular orbital: A MO in
which electron density is concentrated
between two nuclei along the axis joining
them and is cylindrically symmetrical.
Covalent Bonding-Combined VB & MO
• Figure 1.11 A MO energy diagram for
H2. (a) Ground state and (b) lowest
excited state.
Covalent Bonding-Combined VB & MO
• Antibonding MO: A MO in which
electrons have a higher energy than
they would in isolated atomic orbitals.
VB: Hybridization of Atomic Orbitals
• A principle of VB theory is that bonds are created by
the overlap of atomic orbitals.
– Therefore in VB theory, bonds are localized between
adjacent atoms rather than delocalized over several atoms
as in MO theory.
– The VB model correlates with Lewis pictures where two
electrons are visualized between atoms as a bond.
– However, localization of bonds between atoms presents
the following problem.
– In forming covalent bonds, atoms of C, N, and O use 2s
and 2p atomic orbitals.
– If these atoms used these orbitals to form bonds, we
would expect bond angles of approximately 90°.
– However, we rarely observe these bond angles.
VB: Hybridization of Atomic
Orbitals
• Instead, we find bond angles of approximately
109.5° in molecules with only single bonds, 120°
in molecules with double bonds, and 180° in
molecules with triple bonds.
• Linus Pauling proposed that atomic orbitals for
each atom combine to form new atomic orbitals,
called hybrid orbitals, which form bonds by
overlapping with orbitals from other atoms.
• Hybrid orbitals are formed by combinations of
atomic orbitals by a process called hybridization.
VB: Hybridization of Atomic
Orbitals
Energy
– The number of hybrid orbitals formed is equal to
the number of atomic orbitals combined.
– Elements of the 2nd period form three types of
hybrid orbitals, designated sp3, sp2, and sp.
– The mathematical combination of one 2s atomic
orbital and three 2p atomic orbitals forms four
equivalent sp3 hybrid orbitals.
2p
sp3
2s
sp 3 Hybridization, with electron population for
carbon to form four single bonds
VB: Hybridization of Atomic
Orbitals
• Figure 1.12 sp3 Hybrid orbitals. (a) Computed and
(b) cartoon three-dimensional representations. (c)
Four balloons of similar size and shape tied
together, will assume a tetrahedral geometry.
VB: Hybridization of Atomic
Orbitals
• Figure 1.13 Orbital overlap pictures of
methane, ammonia, and water.
VB: Hybridization of Atomic Orbitals
Energy
• The mathematical combination of one 2s atomic
orbital wave function and two 2p atomic orbital
wave functions forms three equivalent sp2 hybrid
orbitals.
2p
2p
sp2
2s
sp 2 Hybridization, with electron
population for carbon to form double
bonds
VB: Hybridization of Atomic Orbitals
• Figure 1.14 sp2 Hybrid orbitals and a single 2p
orbital on an sp2 hybridized atom.
VB: Hybridization of Atomic Orbitals
• VSEPR tells us that
BH3 is trigonal planar,
with 120° H-B-H bond
angles. In BH3 the
unhybridized 2p orbital
is empty.
VB: Hybridization of Atomic
Orbitals
Energy
• The mathematical combination of one 2s
atomic orbital and one 2p atomic orbital gives
two equivalent sp hybrid orbitals.
2p
2p
sp
2s
sp Hybridization, with electron
population for carbon to form
triple bonds
VB: Hybridization of Atomic
Orbitals
• Figure 1.16 sp Hybrid orbitals and two
2p orbitals on an sp hybridized atom.
Combining VB & MO Theories
• VB theory views bonding as arising from electron
pairs localized between adjacent atoms. These
pairs create bonds.
• Further, organic chemists commonly use atomic
orbitals involved in three hybridization states of
atoms (sp3, sp2, and sp) to create orbitals to match
the experimentally observed geometries.
• How do we make orbitals that contain electrons that
reside between adjacent atoms? For this, we turn
back to MO theory.
Combining VB & MO Theories
• To create orbitals that are localized between
adjacent atoms, we add and subtract the atomic
orbitals on the adjacent atoms, which are aligned to
overlap with each other.
• Consider methane, CH4. The sp3 hybrid orbitals of
carbon each point to a 1s orbital of hydrogen and,
therefore, we add and subtract these atomic
orbitals to create molecular orbitals.
• As with H2, one resulting MO is lower in energy
than the two separated atomic orbitals, and is
called a bonding s orbital. The other is higher in
energy and is antibonding.
Combining VB & MO Theories
• Figure 1.17 Molecular orbital mixing diagram for
creation of any C-C sbond.
Combining VB & MO Theories
• This approach is used to create C-H s bonds.
• CH3CH3 contains 1 C-C s bond and 6 C-H s bonds.
Combining VB & MO Theories
• A double bond uses sp2 hybridization.
• In ethylene, C2H4. Carbon uses a combination of
sp2 hybrid orbitals and the unhybridized 2p orbital
to form double bonds.
Combining VB & MO Theories
• Figure 1.21 MO mixing diagram for the
creation of any C-C p bond.
Combining VB & MO Theories
• A carbon-carbon
triple bond consists
of one s bond
formed by overlap of
sp hybrid orbitals
and two p bonds
formed by the
overlap of parallel 2p
atomic orbitals.
Resonance
:
:
• For many molecules and ions, no single Lewis
structure provides a truly accurate representation.
O:
:O :
H3 C C
and
H3 C C
O:
-
:
:
:O:
-
Ethanoate ion
(acetate ion)
Resonance
• Linus Pauling - 1930s
– Many molecules and ions are best described by
writing two or more Lewis structures.
– Individual Lewis structures are called
contributing structures.
– Connect individual contributing structures by
double-headed (resonance) arrows.
– The molecule or ion is a hybrid of the various
contributing structures.
Resonance
• Examples: equivalent contributing structures.
CH3
O:
CH3
O:
C
: O :-
:
N itrite ion
(equivalent con trib uting
s tru ctures)
C
:
:O :-
:
:
O:
: O :-
O:
:N
:
:N
:
:
:
:O: -
A cetate ion
(equ ivalen t contributin g
s tru ctures)
Resonance
• Curved arrow: A symbol used to show the
redistribution of valence electrons.
• In using curved arrows, there are only two allowed
types of electron redistribution:
– from a bond to an adjacent atom.
– from a lone pair on an atom to an adjacent bond.
• Electron pushing is critical throughout organic
chemistry.
Resonance
• All contributing structures must
1. have the same number of valence electrons.
2. obey the rules of covalent bonding:
– no more than 2 electrons in the valence shell of
H.
– no more than 8 electrons in the valence shell of
a 2nd period element.
3. differ only in distribution of valence electrons; the
position of all nuclei must be the same.
4. have the same number of paired and unpaired
electrons.
Resonance
• The carbonate ion
– Is a hybrid of three equivalent contributing
structures.
– The negative charge is distributed equally
among the three oxygens.
Resonance
• Preference 1: filled valence shells
– Structures in which all atoms have filled valence
shells contribute more than those with one or
more unfilled valence shells.
CH3
+
O
••
C
H
H
Greater contribution;
both carbon and oxygen have
complete valence s hells
••
CH3 O
••
+
C
H
H
Lesser contribution;
carbon has only 6 electrons
in its valence s hell
Resonance
• Preference 2: maximum number of covalent
bonds
– Structures with a greater number of covalent
bonds contribute more than those with fewer
covalent bonds.
CH3
+
O
••
••
C
H
H
Greater contribution
(8 covalent bonds)
CH3 •O
•
+
C
H
H
Lesser contribution
(7 covalent bonds)
Resonance
• Preference 3: least separation of unlike
charge
– Structures with separation of unlike charges
contribute less than those with no charge
separation.
Greater contribution
(no separation of
unlike charges)
:
:
O:
CH3 -C- CH3
:O: -
CH3 -C- CH3
Lesser contribution
(separation of unlike
charges)
Resonance
• Preference 4: negative charge on the more
electronegative atom.
– Structures that carry a negative charge on the
more electronegative atom contribute more than
those with the negative charge on a less
electronegative atom.
O
(1)
C
H3 C
O
O
CH3
(a)
Less er
con trib ution
(2)
C
H3 C
CH3
(b)
Greater
contribu tion
C
H3 C
CH3
(c)
S hould n ot
be d raw n
Bond Lengths and Bond Strengths
Name
Formula
H H
Ethane
Bond
sp 3-sp 3
153.2
C-H
sp 3-1s
111.4
C-C
sp 2-sp 2, 2p-2p
133.9
C-H
sp 2-1s
110.0
sp -sp , two 2 p-2p
sp -1s
121.2
109.0
H H
Ethene
H
C
H
Ethyne
C
H
C-C
H-C
Bond Length
(pm)
C-C
H- C- C-H
H
Orbital
Overlap
C-H
C-H
1.10: Bond Lengths and
Strengths
•
•
•
•
Alkyne C-C shorter than Alkene C-C
Alkene C-C shorter than Alkane C-C
Alkyne C-H shorter than Alkene C-H
Alkene C-H shorter than Alkane C-H
• Shorter bonds are stronger
• But sigma bonds are stronger than pi
FAKTOR-FAKTOR YANG MENENTUKAN DENSITAS
ELEKTRON DALAM MOLEKUL ORGANIK
•
•
•
•
•
Efek Induksi
Mesomeri/delokalisasi elektron
Resonansi
Polarisabilitas
Sterik/Ruang
PEMAKSAPISAHAN
• Homolitik: menghasilkan radikal
• Heterolitik: menghasilkan karbokation
dan karboanion
KAJIAN MEKANISME
REAKSI
Chemistry 30A
Introduction to Organic Chemistry
Spring 2009
MWF 12-12:50 CS50
Instructor: Dr. Arif Karim
Office: 3077D Young Hall
Office Hours: M 3-5 and by appointment
Email: [email protected]